{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:T4FGUWLN32QLNKTFEZYSK2ZNCI","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"b218529f03087caad85aba6286ea3112153b9008ca3af5d740c826c6795f3a15","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2018-11-13T14:59:48Z","title_canon_sha256":"844a26223dfb775a97013b9186c2100d920583e34b2a37093da6b99f2627fd5a"},"schema_version":"1.0","source":{"id":"1811.05351","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.05351","created_at":"2026-05-17T23:53:04Z"},{"alias_kind":"arxiv_version","alias_value":"1811.05351v2","created_at":"2026-05-17T23:53:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.05351","created_at":"2026-05-17T23:53:04Z"},{"alias_kind":"pith_short_12","alias_value":"T4FGUWLN32QL","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"T4FGUWLN32QLNKTF","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"T4FGUWLN","created_at":"2026-05-18T12:32:53Z"}],"graph_snapshots":[{"event_id":"sha256:456c3c2540e409a6d81ff915bd649b3cc1ac16900db28561243b6214f32ebe92","target":"graph","created_at":"2026-05-17T23:53:04Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We investigate the performance of a deterministic GREEDY algorithm for the problem of maximizing functions under a partition matroid constraint. We consider non-monotone submodular functions and monotone subadditive functions. Even though constrained maximization problems of monotone submodular functions have been extensively studied, little is known about greedy maximization of non-monotone submodular functions or monotone subadditive functions.\n  We give approximation guarantees for GREEDY on these problems, in terms of the curvature. We find that this simple heuristic yields a strong approx","authors_text":"Andreas G\\\"obel, Francesco Quinzan, Frank Neumann, Ralf Rothenberger, Tobias Friedrich","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2018-11-13T14:59:48Z","title":"Greedy Maximization of Functions with Bounded Curvature under Partition Matroid Constraints"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.05351","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:fc4d806514a7f5dd55c1f676bc52d0f22b3a361c9a4a678aa220194741702084","target":"record","created_at":"2026-05-17T23:53:04Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"b218529f03087caad85aba6286ea3112153b9008ca3af5d740c826c6795f3a15","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2018-11-13T14:59:48Z","title_canon_sha256":"844a26223dfb775a97013b9186c2100d920583e34b2a37093da6b99f2627fd5a"},"schema_version":"1.0","source":{"id":"1811.05351","kind":"arxiv","version":2}},"canonical_sha256":"9f0a6a596ddea0b6aa652671256b2d1205d39dee8f19821f15651077f3728b02","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9f0a6a596ddea0b6aa652671256b2d1205d39dee8f19821f15651077f3728b02","first_computed_at":"2026-05-17T23:53:04.337895Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:04.337895Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wu/RfLQnZ9svnFz3MCZGMIOMg3MRHxohFFujKbMlWLxhWSzCcOgg+PFquMjAG6kCQaBNU4iXs73uLlF5tIK5Dg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:04.338325Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.05351","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fc4d806514a7f5dd55c1f676bc52d0f22b3a361c9a4a678aa220194741702084","sha256:456c3c2540e409a6d81ff915bd649b3cc1ac16900db28561243b6214f32ebe92"],"state_sha256":"978615ea5fff7275c66bd6344c3a9de05b5fd5f67587c1cef153a8c88c3991e0"}